> turfg.mod1 <- aov(chlrfl ~ block + nitrogen + block:nitrogen + years + years:nitrogen)
> summary(turfg.mod1)
               Df Sum Sq Mean Sq F value    Pr(>F)    
block           1  0.510  0.5104  2.3786   0.16158    
nitrogen        3 37.325 12.4415 57.9799 9.036e-06 ***
years           2  3.816  1.9079  8.8913   0.00927 ** 
block:nitrogen  3  1.258  0.4193  1.9540   0.19957    
nitrogen:years  6  4.154  0.6924  3.2265   0.06460 .  
Residuals       8  1.717  0.2146                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> 
> turfg.mod2 <-  aov(chlrfl ~ nitrogen*years + Error(block/nitrogen))
> summary(turfg.mod2)

Error: block
          Df  Sum Sq Mean Sq F value Pr(>F)
Residuals  1 0.51042 0.51042               

Error: block:nitrogen
          Df Sum Sq Mean Sq F value   Pr(>F)   
nitrogen   3 37.325 12.4415  29.672 0.009896 **
Residuals  3  1.258  0.4193                    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Error: Within
               Df Sum Sq Mean Sq F value  Pr(>F)   
years           2 3.8158 1.90792  8.8913 0.00927 **
nitrogen:years  6 4.1542 0.69236  3.2265 0.06460 . 
Residuals       8 1.7167 0.21458                   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> 
> library(lme4)
> 
> turfg.mod3 <- lmer(chlrfl ~ nitrogen*years + (1|block/nitrogen))
> summary(turfg.mod3)
Linear mixed model fit by REML 
Formula: chlrfl ~ nitrogen * years + (1 | block/nitrogen) 
   AIC   BIC logLik deviance REMLdev
 56.78 74.45 -13.39    20.29   26.78
Random effects:
 Groups         Name        Variance  Std.Dev.
 nitrogen:block (Intercept) 0.0682407 0.261229
 block          (Intercept) 0.0075926 0.087136
 Residual                   0.2145833 0.463231
Number of obs: 24, groups: nitrogen:block, 8; block, 2

Fixed effects:
                 Estimate Std. Error t value
(Intercept)        3.8500     0.3811  10.103
nitrogen2          1.7500     0.5318   3.291
nitrogen3          2.6500     0.5318   4.983
nitrogen4          3.5000     0.5318   6.581
years5             1.5000     0.4632   3.238
years8             1.2500     0.4632   2.698
nitrogen2:years5  -1.2500     0.6551  -1.908
nitrogen3:years5  -2.0000     0.6551  -3.053
nitrogen4:years5  -0.2500     0.6551  -0.382
nitrogen2:years8  -1.0500     0.6551  -1.603
nitrogen3:years8   0.0500     0.6551   0.076
nitrogen4:years8  -0.1500     0.6551  -0.229

Correlation of Fixed Effects:
            (Intr) ntrgn2 ntrgn3 ntrgn4 years5 years8 ntr2:5 ntr3:5 ntr4:5
nitrogen2   -0.698                                                        
nitrogen3   -0.698  0.500                                                 
nitrogen4   -0.698  0.500  0.500                                          
years5      -0.608  0.436  0.436  0.436                                   
years8      -0.608  0.436  0.436  0.436  0.500                            
ntrgn2:yrs5  0.430 -0.616 -0.308 -0.308 -0.707 -0.354                     
ntrgn3:yrs5  0.430 -0.308 -0.616 -0.308 -0.707 -0.354  0.500              
ntrgn4:yrs5  0.430 -0.308 -0.308 -0.616 -0.707 -0.354  0.500  0.500       
ntrgn2:yrs8  0.430 -0.616 -0.308 -0.308 -0.354 -0.707  0.500  0.250  0.250
ntrgn3:yrs8  0.430 -0.308 -0.616 -0.308 -0.354 -0.707  0.250  0.500  0.250
ntrgn4:yrs8  0.430 -0.308 -0.308 -0.616 -0.354 -0.707  0.250  0.250  0.500
            ntr2:8 ntr3:8
nitrogen2                
nitrogen3                
nitrogen4                
years5                   
years8                   
ntrgn2:yrs5              
ntrgn3:yrs5              
ntrgn4:yrs5              
ntrgn2:yrs8              
ntrgn3:yrs8  0.500       
ntrgn4:yrs8  0.500  0.500
> anova(turfg.mod3)
Analysis of Variance Table
               Df  Sum Sq Mean Sq F value
nitrogen        3 19.1012  6.3671 29.6717
years           2  3.8158  1.9079  8.8913
nitrogen:years  6  4.1542  0.6924  3.2265